One-to-One Matching Problems with Location Restrictions

Wouter Vergote

No 2015054, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: This paper introduces a novel set of one-to-one matching problems: matchings subject to location restrictions. When scarcity of matching locations exists some agents may want to form a new partnership without being able to implement it. In this general setting we develop two stability concepts, direct and (coalition) ex- change* stability, akin to Gale Shapley stability and exchange stability (Alcalde, 1995) respectively. We show that coalition-exchange* stability is a refinement of direct stability. When no location scarcity exists then direct stability is equivalent to Gale Shapley stability and coalition-exchange* stability is equivalent to requiring both exchange stability (Alcalde, 1995) and Gale Shapley stability. We show that the set of coalition-exchange* stable matchings is a superset of the farsighted core, and equal to the farsighted core if locations are not scarce and the matching problem is individually rational. The paper also shows that an exchange* stable set can not be a strict subset of a farsighted stable set and provides an example of a roommate problem in which no farsighted stable set exists while an exchange* stable set does exist. Finally, the paper obtains that deciding whether the farsighted core of an individually rational roommate problem exists is NP-complete.

Keywords: One-to-one Matching; Direct Dominance; Exchange Dominance; Indirect Dominance (search for similar items in EconPapers)
JEL-codes: C71 C78 (search for similar items in EconPapers)
Date: 2015-06-08
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